It will first be shown that the topology will no longer switch after a finite number of switches. We prove by contradiction. Assume that the topology switches all the time.
Firstly, it will be proven that the topology will no longer switch after a finite number of switches. We prove it through proof to the contrary. Assuming the topology keeps switching.
First, it will be proved that the topology will not switch after a limited number of switches. We prove it by reducing to absurdity. Assume that the topology keeps switching.